Inequalities & Intervals
Given
A= 1, 2, 3, 4, 5
B= 1, 3, 5, 7, 9
What is A ∪ B? What is A ∩ B?
A ∪ B=1, 2, 3, 4, 5, 7, 9
A ∩ B=1, 3,5
Is the given point on the line?
(6, 10) y=x+4
Yes
Solve for x:
3x+2-2x=7x+7-4
x=-1/6
True or False:
-√ 25 = √ -25
False
There are 40 people in a class. If 1/8 of them are math majors, how many people are NOT math majors?
35
Graph using a number line:
x+2>0 AND x-3≤0
Should have: ( at x=-2, ] at x=3
Graph the following equation:
y=2x-2
Should have: point at (0, 2) and slope of +2
Factor:
f(x)=x2-5x+6
f(x)=(x-2)(x-3)
Simplify the following expression:
a3b2c/ab2c3
a2/c2
Jordyn has a supply of paper consisting of 120 packages. If you buy 15% of the supply, how many packages did you buy?
18
Graph using a number line:
2x-4>0 OR x+7<0
Should have: ) at x=-7, ( at x=2
Put the following equation into slope-intercept form:
y-4=2(x-3)
y=2x-2
Expand the following:
(xy+x)(y+4)
xy2+5xy+4x
Simplify each:
1) 2√50 2) 3√32
1) 10√2 2) 2 3√4
A 5lb bucket is placed on a scale, and 1lb apples are placed inside of the bucket. Find an expression for the total weight in terms if the number of apples, A?
A+5
Solve the given inequality:
0≤x+2<4
-2≤x<2
Write the equation of a line in point-slope form using the following:
m=1/2 containing (4, -2)
y+2=1/2(x-4)
Factor the following:
f(x)=x2-9
f(x)=(x+3)(x-3)
Simplify the following:
(xy+z)(y2+xz)
xy3+x2yz+y2z+xz2
Jaime sells printers at a rate of $150 per printer with a set $30 delivery fee with any purchase. What is m (slope) and what does it represent? What is b (y-intercept)?
m=150, price per printer
b=30, flat delivery fee
What is the domain of the function in interval notation:
f(x)=(x+4)/(x-3)
x: (-∞ , 3)U(3,∞ )
Find the y-intercept of the line containing:
(1, 0) and (3, 4)
b=-2 OR (0, -2)
Which of the following is the expanded form of the identity: a3+b3
a) (a-b)(a+b)(a+b)
b) (a-b)(a2+ab+b2)
c) (a+b)(a2-ab+b2)
d) (a+b)(a2+ab+b2)
C
Add the following (combine to one term):
(2ac/b2) + (a/bc)
(2ac2+ab)/b2c
You start walking from your house at a rate of 4mph. Your friend had a 4 mile head start and it walking at 2mph. After how many hours do you catch up? (Hint: graph)
2 hours